The momentum distribution $n(k)$ and condensate fraction $\frac{{N}_{0}}{N}$ for liquid helium and for a charged Bose gas are evaluated in perturbation theory through second order in $\frac{1}{\sqrt{N}}$ . For liquid helium at normal vapor pressure, to this order in perturbation theory, we obtain unphysical, negative values for $n(k)$ . This result will be discussed in detail.The momentum distribution $n(k)$ and condensate fraction $\frac{{N}_{0}}{N}$ for liquid helium and for a charged Bose gas are evaluated in perturbation theory through second order in $\frac{1}{\sqrt{N}}$. For liquid helium at normal vapor pressure, to this order in perturbation theory, we obtain unphysical, negative values for $n(k)$. This result will be discussed in detail.

Physical review. B, Solid stateJun 1, 19752 citations

Boson-fermion pairing and condensation in two-dimensional Bose-Fermi mixtures

L. Pisani, Pietro Bovini, Fabrizio Pavan +1 more

We consider a mixture of bosons and spin-polarized fermions in two dimensions at zero temperature with a tunable Bose-Fermi attraction. By adopting a diagrammatic T T -matrix approach, we analyze the behavior of several thermodynamic quantities for the two species as a function of the density ratio and coupling strength, including the chemical potentials, the momentum distribution functions, the boson condensate density, and the Tan’s contact parameter. By increasing the Bose-Fermi attraction, we find that the condensate is progressively depleted and Bose-Fermi pairs form, with a small fraction of condensed bosons surviving even for strong Bose-Fermi attraction. This small condensate proves sufficient to hybridize molecular and atomic states, producing quasi-particles with unusual Fermi liquid features. A nearly universal behavior of the condensate fraction, the bosonic momentum distribution, and Tan’s contact parameter with respect to the density ratio is also found.We consider a mixture of bosons and spin-polarized fermions in two dimensions at zero temperature with a tunable Bose-Fermi attraction. By adopting a diagrammatic T T -matrix approach, we analyze the behavior of several thermodynamic quantities for the two species as a function of the density ratio and coupling strength, including the chemical potentials, the momentum distribution functions, the boson condensate density, and the Tan’s contact parameter. By increasing the Bose-Fermi attraction, we find that the condensate is progressively depleted and Bose-Fermi pairs form, with a small fraction of condensed bosons surviving even for strong Bose-Fermi attraction. This small condensate proves sufficient to hybridize molecular and atomic states, producing quasi-particles with unusual Fermi liquid features. A nearly universal behavior of the condensate fraction, the bosonic momentum distribution, and Tan’s contact parameter with respect to the density ratio is also found.

arXiv:2405.05029SciPost PhysicsMar 3, 20254 citations

Statistical mechanics of the gas–liquid condensation in the attractive Bose gas

Shun-ichiro Koh

Physica B Condensed MatterMay 1, 20034 citations

On the Momentum Distribution and Condensate Fraction in the Bose Liquid

Alexander Yu. Cherny, Arkady A Shanenko

The model recently proposed in Ref.1 is used to derive linear integro– differential equations whose solutions provide reasonable estimates for the momentum distribution and condensate fraction in interacting many–boson system at zero temperature. An advantage of these equations is that they can be employed in the weak coupling regime and beyond. As an example, analytical treatment of the weak coupling case is given. PACS: 05.30.Jp, 67.90.+z A new way of investigating spatial particle correlations has recently been proposed for the many–boson system in the ground state [1]. It results in integro–differential equations for the pair distribution function. They accurately take into account the short–range boson correlations and, in the weak coupling regime, yield thermodynamics which reasonably agreesThe model recently proposed in Ref.1 is used to derive linear integro– differential equations whose solutions provide reasonable estimates for the momentum distribution and condensate fraction in interacting many–boson system at zero temperature. An advantage of these equations is that they can be employed in the weak coupling regime and beyond. As an example, analytical treatment of the weak coupling case is given. PACS: 05.30.Jp, 67.90.+z A new way of investigating spatial particle correlations has recently been proposed for the many–boson system in the ground state [1]. It results in integro–differential equations for the pair distribution function. They accurately take into account the short–range boson correlations and, in the weak coupling regime, yield thermodynamics which reasonably agrees

Jan 1, 19970 citations

The momentum distribution

n(k)

and condensate fraction

\frac{{N}_{0}}{N}

for liquid helium and for a charged Bose gas are evaluated in perturbation theory through second order in

\frac{1}{\sqrt{N}}

. For liquid helium at normal vapor pressure, to this order in perturbation theory, we obtain unphysical, negative values for

n(k)

. This result will be discussed in detail.